Yielding link, particularly for eccentrically braced frames

ABSTRACT

A structural yielding link, particularly for use in an eccentrically braced frame arrangement or in a linked column frame arrangement having a first end having a means for connecting to a face of a first beam and a second end having a means for connecting to a face of a second beam; a first variable cross-section portion and a second variable cross-section portion extending from the first end and from the second end, respectively; and a constant cross-section portion joining the first variable cross-section portion and the second variable cross-section portion.

FIELD OF THE INVENTION

The invention relates generally to building frame structures, andparticularly to yielding links for use is building frame structures,especially eccentrically braced frames or linked column frames.

BACKGROUND OF THE INVENTION

Eccentrically braced frames (EBFs) are a commonly used, high-ductilitylateral load resisting system, generally implemented in steel buildingconstructions. The brace(s) in an EBF are arranged such that at one endthe brace(s) are connected to a frame node and at the other end thebrace(s) are connected to a beam. In the case where the EBF has onebrace per frame, the brace work point is located away from the nodedefined by the beam column intersection. In the case where the EBF hastwo braces per frame, the braces do not share a node at center of thebeam. Rather, each brace is slightly more inclined, thus moving the twobrace end points away from the centre of the beam. In bothconfigurations, the eccentric brace geometry results in shear andbending being applied to a short portion of the continuous beam. Thisportion of the beam is commonly referred to as the link, or yieldinglink. During an earthquake, the system is designed such that the linkyields in shear or flexure (or a combination of both), thereby limitingthe force that can develop in the other structural elements andabsorbing seismic energy in a stable manner.

Typically, the link portions of EBFs have been wide flange (W-sections),rectangular hollow sections (HSS), or built-up box sections. EBFsexhibit excellent ductility capacity and perform well after anearthquake. However, after a severe seismic event, the links aresomewhat damaged and can require repair or replacement. This led to thedevelopment of replaceable links for EBFs.

In an EBF with replaceable links, the link is a separate component fromthe rest of the beam element(s). The replaceable link is the yieldingelement of this system and the remaining beam element(s) are intended toremain elastic. This component is bolted or welded to the beam such thatthere is a predominantly rigid connection capable of transmitting theshear force or bending moment required to yield the link element. Priorresearch on replaceable links has focused on link elements created fromweld-fabricated rolled sections such as W-sections, channels,rectangular hollow structural sections, and build-up box sections. Allof these concepts have been continuous, prismatic, constantcross-section sections that yield either in constant shear or inflexural hinging at the ends of the links.

A linked column frame is an arrangement that utilizes replaceable linksin a modified structural configuration. The behaviour of the link in thelinked column frame is the same as it is in the eccentrically bracedframe, thus any link developed for eccentrically braced frames may beequally applicable to a linked column frame, and indeed have beenapplied to link column frames in the prior art.

It is an object of the invention to provide a replaceable yielding linkproviding at least one improvement over the prior art.

SUMMARY OF THE INVENTION

According to one embodiment of the invention, there is provided astructural yielding link having a first end having a means forconnecting to a face of a first beam or column and a second end having ameans for connecting to a face of a second beam or column; a firstvariable cross-section portion and a second variable cross-sectionportion extending from the first end and from the second end,respectively; and a constant cross-section portion joining the firstvariable cross-section portion and the second variable cross-sectionportion.

In one aspect of the invention, the structural yielding link is used inan eccentrically braced frame arrangement or in a linked column framearrangement.

In another aspect of the invention, the first and the second variablecross-section portions are hollow along at least a portion of lengthsthereof.

In another aspect of the invention, the first variable cross-sectionportion and the second variable cross-section portion have across-section tapering from the respective first and second end portionstowards the constant cross-section portion such that a width of thefirst and second variable cross-section portions at the respective firstand second end portions is greater than a width at the constantcross-section portion.

In another aspect of the invention, the first and the second variablecross-section portions are hollow and have an interior wall thicknesswhich is greater at the first and second end portions, respectively thanproximate the constant-cross section portion.

In another aspect of the invention, the variable cross-section portionsare designed, sized and otherwise dimensioned to promote nearsimultaneous yielding along a substantial portion of the yielding linkwhen subjected to a linearly varying bending moment diagram.

In another aspect of the invention, the first and the second variablecross-section portions have a width defined by a higher-order function;whereby the higher-order function promotes yielding of the link when thelink is subjected to load(s) causing a linearly varying bending momentdiagram.

In another aspect of the invention, the first and the second variablecross-section portions are defined such that the cross sectional areaalong the length of the link is constant; whereby the constant crosssectional area promotes a constant axial strain along the length of thelink when the link is subjected to any axial load.

In another aspect of the invention, the constant cross sectional area isachieved by a flange located at the flexural neutral axis of the crosssection.

In another aspect of the invention, there is further provided atransition region between the first and second ends and the first andsecond variable cross-section portions, respectively; where thetransition region includes a thickened material portion for limitingstress and strain occurring during yielding of the link from propagatingto the means for connecting to the end faces of the first and secondbeams.

In another aspect of the invention, the variable cross-section portionsare designed, sized and otherwise dimensioned to promote yielding alonga substantial portion of the yielding link.

In another aspect of the invention, the first and the second variablecross-section portions are hollow and have an interior wall thicknesswhich is constant throughout the first and second variable cross-sectionportions.

In another aspect of the invention, the first variable cross-sectionportion and the second variable cross-section portion have across-section tapering from the respective first and second end portionstowards the constant cross-section portion such that a depth of thefirst and second variable cross-section portions at the respective firstand second end portions is greater than a depth at the constantcross-section portion.

According to another embodiment of the invention, there is provided aneccentrically braced frame arrangement having a first column and asecond column; a beam connecting the first column and the second column;the beam having a first portion connected to the first column, a secondportion connected to the second column and a yielding link connectingthe first portion and the second portion; at least one brace having anode end connected proximate an end of the first column and another endconnected to an end of the first portion proximate the yielding link;wherein the yielding link includes a first end having a means forconnecting to an end face of the first portion and a second end having ameans for connecting to an end face of the second portion; a firstvariable cross-section portion and a second variable cross-sectionportion extending from the first end and from the second end,respectively; and a constant cross-section portion joining the firstvariable cross-section portion and the second variable cross-sectionportion.

In one aspect of this embodiment, the first and the second variablecross-section portions are hollow along at least a portion of lengthsthereof.

In another aspect of this embodiment, the first variable cross-sectionportion and the second variable cross-section portion have across-section tapering from the respective first and second end portionstowards the constant cross-section portion such that a width of thefirst and second variable cross-section portions at the respective firstand second end portions is greater than a width at the constantcross-section portion.

In another aspect of this embodiment, the first and the second variablecross-section portions are hollow and have an interior wall thicknesswhich is greater at the first and second end portions, respectively thanproximate the constant-cross section portion.

In another aspect of this embodiment, the variable cross-sectionportions are designed, sized and otherwise dimensioned to promoteyielding along a substantial portion of the yielding link.

In another aspect of this embodiment, the first and the second variablecross-section portions have a width defined by a higher-order function;whereby the higher-order function promotes yielding of the link when thelink is subjected to load(s) causing a linearly varying bending momentdiagram.

In another aspect of this embodiment, the first and the second variablecross-section portions are defined such that the cross sectional areaalong the length of the link is constant; whereby the constant crosssectional area promotes a constant axial strain along the length of thelink when the link is subjected to any axial load.

In another aspect of this embodiment, the constant cross sectional areais achieved by a flange located at the flexural neutral axis of thecross section.

In another aspect of this embodiment, there is further provided atransition region between the first and second ends and the first andsecond variable cross-section portions, respectively; where thetransition region includes a thickened material portion for limitingstress and strain occurring during yielding of the link from propagatingto the means for connecting to the end faces of the first and secondbeams.

In another aspect of this embodiment, the variable cross-sectionportions are designed, sized and otherwise dimensioned to promoteyielding along a substantial portion of the yielding link.

In another aspect of this embodiment, wherein the first and the secondvariable cross-section portions are hollow and have an interior wallthickness which is constant throughout the first and second variablecross-section portions.

In another aspect of this embodiment, the first variable cross-sectionportion and the second variable cross-section portion have across-section tapering from the respective first and second end portionstowards the constant cross-section portion such that a depth of thefirst and second variable cross-section portions at the respective firstand second end portions is greater than a depth at the constantcross-section portion.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the attached Figures, wherein:

FIG. 1 is an elevation view of a yielding link in an eccentricallybraced frame according to one embodiment of the invention.

FIGS. 2A, 2B and 2C show side, top and end views, respectively, of theyielding link of FIG. 1.

FIG. 3 is a perspective view of the yielding link of FIG. 1.

FIG. 4 is an elevation view of a yielding link in an eccentricallybraced frame according to another embodiment of the invention.

FIGS. 5A, 5B and 5C show side, top and end views, respectively, of theyielding link of FIG. 4.

FIG. 6 is a perspective view of the yielding link of FIG. 4.

FIG. 7 is an elevation view of a yielding link in a single-braceeccentrically braced frame according to another embodiment of theinvention.

FIGS. 8A, 8B and 8C show side, top and end views, respectively, of theyielding link of FIG. 7.

FIG. 9 is a perspective view of the yielding link of FIG. 7.

FIG. 10 is an elevation view of a yielding link in a linked column frameaccording to another embodiment of the invention.

FIGS. 11A, 11B and 11C show side, top and end views, respectively, ofthe yielding link of FIG. 10.

FIG. 12 is a perspective view of the yielding link of FIG. 10.

FIG. 13 is a reference diagram showing key variables in the design ofthe yielding link according to the invention.

DETAILED DESCRIPTION

Embodiments of the invention provide a replaceable yielding link with across-section that varies along at least a portion of the length of theyielding link. The yielding link is intended to be used in eccentricallybraced frame (EBF) arrangements, or in linked column frame arrangementswhich exhibit similar structural responses to force-applying events asEBF arrangements. For the purposes of this disclosure, the terms “link”and “yielding link” are used interchangeably. The cross-section of thelink is preferably shaped, and otherwise dimensioned such that thechange in moment resistance along the length of the link substantiallymatches the moment diagram that results from the applied forces. Thisenables the link to yield in flexure along a substantial portion of itslength, thereby reducing the inelastic strains resulting from a givenamount of plastic link rotation, when compared to the prismatic,constant cross-section links of the prior art. Reducing the inelasticstrains in the link increases the displacement capacity of the link andits resistance to low cycle fatigue fractures, thus increasing theductility of the EBF as a whole. Reducing the inelastic strains alsoenables the design of more compact, efficient links that provide equalor better performance when compared to the prismatic, constantcross-section links of the prior art. This compact design results atleast in easier transport of the link and facilitates replacementfollowing yielding.

A variable cross-section which promotes yielding along substantially thefull length of the link could be achieved in a number of ways. Forexample, if the cross-section is rectangular or square shaped, thelink's width out of the plane of the frame could be varied, the link'sdepth could be varied, or the thickness of the link's walls could bevaried. Any combination of these could also result in a shape thatpromotes near simultaneous yielding along substantially the full lengthof the link.

The theoretical concept of varying the cross-sectional shape of abuilding element to promote spread in yielding or for use as energydissipation mechanisms in base isolated structures has been accomplishedin other prior art applications. (For example, see (i) Tsai et al. 1993.Design Of Steel Triangular Plate Energy Absorbers For Seismic-ResistantConstruction. Earthquake Spectra. Vol. 9, No. 3: pp. 505-528; (ii) Grayet al. 2014. Cast Steel Yielding Brace System For Concentrically BracedFrames: Concept Development And Experimental Validations. Vol. 140. No.4: Paper Number 04013094; and (iii) Japanese Patent Application No.62-051290 (Publication No. 63-219928) filed Mar. 6, 1987 by KajimaCorp.) However, to the knowledge of the applicants, varyingcross-sections have not been used in any form of eccentrically bracedframes to increase performance of the yielding link elements, nor havethey been used as link elements in a linked column frame exhibitingbehaviour analogous to eccentrically braced frames. Furthermore, theadaptations and structural details described herein relatingparticularly to improving any one of performance, efficiency or ease ofconstruction of the link implemented within an eccentrically bracedframe or a linked column frame differ from the prior art of which theapplicant is aware.

Embodiments of the link as herein described are intended to replace thecontinuous beam yielding element of an eccentrically braced frame with areplaceable element. The link is comprised of a yielding segment and twoconnections, at the ends of the yielding segment. The link is intendedfor the protection of the structural frame of a building from excessivedamage during cyclic dynamic loading conditions (such as an earthquake)by absorbing the majority of the energy and limiting the forces thatmust be resisted by the structure as a whole. Cyclic dynamic loadingconditions refers to repeated cycles of flexural yielding, including theincrease in strength that is expected as the replaceable link reacheslarge inelastic strains (due to over-strength and second-order geometriceffects). When a building using the tapered replaceable link issubjected to such loading conditions, the building structure cyclicallydeforms laterally. These cyclic lateral deformations result in cyclicdeformations in which the yielding segment of the link is in doublecurvature. Under severe loading, the cyclic link deformations cause thelink to yield, and to behave in a non-linear manner.

The yielding segment of the tapered replaceable link is shaped based onthe expected combination of bending, shear and axial forces such that itwill yield flexurally along nearly all of its length. The combination ofthese forces can vary depending on the structural loading, framegeometry, and location of the link (in the centre of the beam, at thebeam column connection, or in a linked column frame). The crosssectional geometry of the link varies along its length (in the directionof the beam axis) such that at any given section its extreme fibers willyield at the same magnitude of externally applied bending moment. Thisbending moment would be considered the yield bending moment. Continuousyielding along the length of the yielding segment is advantageous overyielding at discrete locations along the length of the link, because,for links of equal length, continuous yielding will result in lowerplastic strains for a given link rotation, and therefore higherductility, than prior art links. Increasing the ductility of aneccentrically braced frame link decreases the likelihood for structuralcollapse or expensive structural repair.

In addition, at any point along the length of the link the cross-sectionhas sufficient strength to resist the externally applied shear and axialforces that would be associated with the maximum bending moment thatwould be expected, which is limited by the link's non-linear behaviourand the typical range of deformations for an eccentrically braced framestructure. One possible means of resisting the applied axial forcescould be to select the tapering of the cross section such that, inaddition to matching the flexural resistance to the applied bendingmoment, the cross sectional area of the link remains constant along itsentire length. In this case, the stress resulting from any magnitude ofapplied axial force would be constant along the length of the link. Whenyielding in flexure, such a link would exhibit distributed plasticityalong nearly its entire length, regardless of the magnitude of theapplied axial force. In the presence of variable axial forces, a linkwithout this feature (i.e. a link with a varying cross sectional area)could potentially yield in a discreet location, rather than exhibitinguniformly distributed flexural yielding along its length. One possiblemeans of achieving constant cross sectional area could be a thickenedflange located at the flexural neutral axis of the section. Such aflange would attract much of the applied axial load, but not contributesignificantly to the flexural strength. Another possible means ofachieving constant cross sectional area would be to taper the thicknessof the web(s) or side walls of the section to compensate for loss ofarea resulting from tapering the flange(s) or top and bottom walls ofthe section to achieve flexural yielding along substantially the fulllength of the link.

Further, the transition between the yielding portions of the link andthe end connection region could be thickened or otherwise shaped in sucha manner so as to limit inelastic strain from spreading into theconnection region. This would ensure that yielding only occurs in theyielding portion, thus avoiding fracture in the connection region.

Specific embodiments adhering to these principals will now be described.

Referring now to FIGS. 1-3, there is shown a first embodiment of theinvention in which a yielding link 10 is used to connect adjacent beams12 in an eccentrically braced frame arrangement 5. As described earlier,the frame is considered eccentrically braced since the braces 8 are notconnected at a common working node of the frame 5 at their endsproximate the beams 12. The link 10 has a substantially rectangularcross-section 15 that is hollow along a portion of its length, asindicated by the dashed-line portions 20 in FIGS. 2A and 2B. Variablecross-section portions 25 of the link, beginning proximate either endsof the link have a constant depth and a varying width, and arepreferably hollow throughout, or substantially hollow throughout. In thecentre of the link 10, there is a constant cross-section or solidportion 60, which adjoins the two variable portions 25, and definetermination points 65 of the hollow portions 20. For the purposes ofthis application, “depth” is defined as the direction perpendicular tothe ground on which the frame is assembled or along the z-axis in FIG.3, and “width” is defined as a direction parallel to the ground andperpendicular to the elongate axis of the beams to which the link isattached or along the y-axis in FIG. 3.

The thicknesses of the top 30 and bottom 35 walls of the variableportion varies linearly. That is, the material thickness of the wallbounding a top surface 40 of the variable portion with a top surface ofthe hollow portion 20 is linearly variable, as illustrated. Meanwhile,the thickness of the side walls 45 is held constant. That is, thematerial thickness of the wall bounding the sidewall 50 of the variableportion 25 and the sidewall of the hollow portion 20 is constant.

The variation in the width from w to w1 to w2 of the variable portion 25may be linear in some embodiments, but is most preferably defined by ahigher-order function that is defined to ensure that the hollow portions20 of the link 10 yield simultaneously when subjected to a linearlyvarying, double curvature bending moment diagram, combined with shear,axial, and torsional forces at the ends 55 of the link 10. An exampleand derivation of such a higher order function is provided in theExample further below in this description.

The vertical walls 45 of the hollow sections 20 and the solid centre 60of the yielding portion 70 of the link 10 are designed to have adequateshear and axial strength for the combined forces that could be appliedwithin the expected range of deformations in a typical eccentricallybraced frame building or a link column frame, depending on theapplication. The cross section of the link also includes an optionalflange 57 at the neutral axis that has been shaped, and otherwisedimensioned such that the cross sectional area of the link remainsconstant throughout the yielding portions. The flange 57 is preferablylocated at a mid-region of the link, and extends across the length ofthe link. The transition region 67 between the end connection 55 and theyielding portion 70 of the link 10 includes additional material toincrease the thickness so as to ensure that stress and strain resultingfrom flexural or shear yielding does not propagate into the connectionends 55 during cyclic loading. Practically, the ends 55 and thetransition region 67 are designed, sized, and otherwise dimensioned toprevent failure or yielding of the link 10 at the connection with eitherbeam 12 or at a portion of the link 10 proximate this connection. Thespecific dimensions of the link 10 and sizing of each of the elementsdescribed above will be dependent upon the specific implementation andwill be calculable by one skilled in the art in view of thisdescription.

Referring now to FIGS. 4-6, there is shown a second embodiment of theinvention in which a yielding link 110 is used to connect adjacent beamsin an eccentrically braced frame arrangement 105. The link 110 has asubstantially rectangular cross-section 115 that is hollow along a majorportion of its length, as indicated by the dashed-line portions 120 inFIGS. 5A and 5B. Variable cross-section portions 125 of the link have aconstant depth and a varying width. The varying, and in particular,tapering width as illustrated is designed to promote yielding along theentire length of the variable cross-section portions 125. At the centreof the link 110, there is a solid portion 160, which adjoins the twovariable cross-section portions 125.

The thicknesses of the top 130 and bottom 135 walls of the variablecross-section portion 125 is maintained constant, in distinction to theembodiment of FIGS. 1-3. In this embodiment, the walls of the variablecross-section portion 125 and of the solid portion 160 are designed,sized and otherwise dimensioned to have adequate shear and axialstrength for the combined forces that could theoretically be appliedwithin the expected range of deformations in a typical eccentricallybraced frame structure. Additional details of this embodiment may be asdescribed with respect to the embodiment of FIGS. 1-3.

In a third embodiment of the invention, as illustrated in FIGS. 7-9there is shown a yielding link 210 having a substantially rectangularcross-section 215 that is hollow along all of its length, as indicatedby the dashed-line portions 220 in FIGS. 8A and 8B. Variablecross-section portions 225 of the link have a varying depth and aconstant width and wall thickness within the variable cross-sectionportions 225. The varying, and in particular, tapering depth asillustrated is designed to promote yielding along the entire length ofthe variable cross-section portions 225. At the centre of the link 110,there is a hollow, constant depth portion 260, which adjoins the twovariable cross-section portions 225.

The thicknesses of the top 230 and bottom 235 walls of the variablecross-section portion 225 is maintained constant. The walls of thevariable cross-section portion 225 and of the hollow, constant depthportion 260 are designed, sized and otherwise dimensioned to haveadequate shear and axial strength for the combined forces that couldtheoretically be applied within the expected range of deformations in atypical eccentrically braced frame structure. Additional details of thisembodiment may be as described with respect to the embodiment of FIGS.1-3.

In other contemplated alternatives, the yielding segment of the link mayhave cross-sections other than substantially rectangular cross-sectionsas described in the previous embodiments. The cross-section may be anyshape or configuration that has a variable, and preferably tapered,cross-section such that flexural yielding along a substantial portion ofthe length of the link is promoted. On example of this is shown in theembodiment of FIGS. 10-12 where a link 300 has a primarily “I” shapedcross section. The width w of the flanges 305 of the “I” shape variesalong the length of the link, thus providing for the variablecross-section. The varying cross-section of the flanges 305 is intendedto promote yielding along most of the length of the yielding segment ofthe link. In this embodiment the web 310 of the “I” section is designedto have adequate shear and axial strength for the combined forces thatcould be applied within the expected range of deformations in a typicaleccentrically braced frame building. The thickness of the web 310 istapered along the length of the link such that at any section the yieldmoment matches the applied bending moment (thereby resulting indistributed flexural yielding) and the cross sectional area is constant(thereby resulting in a uniform axial strain along the length).

Other variable cross-sections, and in particular tapered cross-sectionsare also contemplated. Any of the above described embodiments could beused in a variety of eccentrically braced frame configurations (forexample, the link in the centre of the beam or the link at the beamcolumn intersection) or in linked column frame configurations. Othershapes and cross-sections are known in the art, and to which theteachings of this invention in respect of one or more of the variabilityof the cross-sections, the hollow portion within the variablecross-section portion or the solid centre portion having a constantcross-section may be applied to prior art link cross-sectional shapes.This statement is not intended to limit the invention to requiring eachof the variable cross-section portion, hollow portion within thevariable cross-section portion and the constant cross-section centreportion in combination as essential features. Rather, the invention isonly limited by the claims that follow this description.

There are a number of means by which the link can be connected to theother elements of the structural frame, be it the eccentrically bracedframe or a linked column frame. For example, in the embodiment FIG. 1,the link 10 is shown at the centre of a chevron-type eccentricallybraced frame 5. The link 10 is connected to the beams of the frame witha bolted end-plate type connection. To accommodate this type ofconnection the ends of the yielding segment of the link have large,vertically oriented plate elements 7 that bolt to corresponding endplates 3 on the ends of the beam elements of the structural frame. Thisconnection would be designed to have the strength to resist thecombination of bending moment, shear and axial force that would beinduced in the expected range of deformations in a typical eccentricallybraced frame building. Another feature of this implementation would be asmall, protruding extension of the plate extending within the hollow ofthe yielding segment, in order to increase the rigidity at theintersection of the end plate and the yielding segment of the link 10,thereby ensuring the deformations are isolated within the yieldingsegment of the link.

The embodiment of FIG. 4 is also shown at the centre of a chevron typeeccentrically braced frame. This embodiment is connected to the webs ofthe beams of the brace with a bolted shear connection via plates 107.

The link 210 of FIG. 7 is shown at the beam column intersection of asingle brace eccentrically braced frame 205. The link 210 is connectedto the beam and the face of the column via a welded connection. At theend of the yielding portion the walls 230 of the end portions 225 aremade thicker than the walls 230, 235 in the variable cross-sectionportion 225. This additional material thickness is provided to ensurethat yielding does not propagate to the vicinity of the weld. The weldedjoint between the tapered replaceable link and the end plate of thebeam, or the face of the column, can be achieved with fillet welds orgroove welds, or other weld details.

The embodiment of FIG. 10 is shown in a linked column frame 300 havingcolumns 360 and 370 of adjacent column frames, which are linked by thelinks 300. This embodiment is shown with a bolted end plate typeconnection which would bolt to the faces of the two columns in thesystem.

Other end connection configurations are possible but not illustrated,provided the end connection is designed to resist the combination ofbending moment, shear and axial force that would be induced in theexpected range of deformations in a typical eccentrically braced framebuilding, would not change the primary function or behaviour of thereplaceable link.

The various embodiments of the link as herein described may be formed bycasting, which provides a manner for creating the optionally complex orhigher order tapering of the variable cross-section portion of the linkof some embodiments. It is also noteworthy that such casting processespermit for the hollow portions, and variable thickness of certain wallsas described above, as the link can be manufactured to have complex ordetailed geometries both on the outer portions and within the hollowportions as well, such as the varying wall thickness as described insome embodiments above. Casting the link as a single body would alsoeliminate the need to weld various plates together within the yieldingregion. This would eliminate the potential for premature fractures,which is a risk when welds are subjected to large inelastic strain. Castwould also eliminate sharp geometric transitions which could createundesirable stress concentrations in the yielding region.

EXAMPLE

While linear tapered cross-sections are contemplated in the variablecross-section portion of the link, as herein described, there areadditional advantages to providing a tapering which follows a higherorder function in defining segments of the variable cross-section of thelink. In order to implement the variable cross-section link of FIGS.1-3, and in particular with a higher order function defining thetapering and variable cross-section, applicant has contemplated oneexample of defining the profile of the tapering width of the variablecross-section.

Referring to FIG. 13, a profile of the link 1305 is derived from thefollowing derivation defining the profile of the tapering of the widthof the section, b(x), which considers the plastic capacity of theflanges (top and bottom walls) of the box section and ignores the anycontribution from the webs of the box section as being negligible. It isassumed that the link is deformed in double curvature. The assumedapplied shear on the link, V, is combined with the length of the link todefine applied moment at any point, x, along the length of the link. Theapplied moment is in turn used to define profile of the section. Thegeneralized profile of the tapering as a function of the applied shear,V, yield strength of the material, F_(y), depth of the section, d, andthe tapering of the flange thickness, h(x), is presented in thefollowing equation:

${b(x)} = \frac{V\left( {L - {2x}} \right)}{2\; {h(x)}{F_{y}\left\lbrack {d - {h(x)}} \right\rbrack}}$

In the particular embodiment of interest the thickness of each flange,h(x), varies linearly from thick at the end to thin in the middle of theyielding link. The equation describing the flange thickness at anypoint, x, along the length of the yielding portion of the link, ispresented below as a function of the maximum flange thickness, h_(max),minimum flange thickness, h_(min), and the length of the yieldingportion, L_(y):

${h(x)} = {{h_{\max}\left( {1 - \frac{x}{L_{y}}} \right)} + {h_{\min}\frac{x}{L_{y}}}}$

Substituting these two equations would give the specific equationdefining the width of the flange along the length of the link betweenthe connection end (x=0) to the inner end of the yielding portion of thelink (x=L_(y)).

${b(x)} = {\frac{V}{2F_{y}} \times \frac{\left( {L - {2x}} \right)}{\begin{matrix}{{dh}_{\max} - h_{\max}^{2} + \left\lbrack {{- {dh}_{\max}} + {dh}_{\min} + {2h_{\max}^{2}} -} \right.} \\{{\left. {2h_{\max}h_{\min}} \right\rbrack \left( \frac{x}{L_{y}} \right)} - {\left\lbrack {h_{\max} - h_{\min}} \right\rbrack^{2}\left( \frac{x}{L_{y}} \right)^{2}}}\end{matrix}}}$

The side walls of the link include a ridge located at the section'sneutral axis which is proportioned such that the cross-sectional area ofthe link at any location is the same despite the tapering width of thelink. The area of the external flanges, A_(flanges)(x), was determinedbased on the following equation:

A _(flanges)(x)=2[b(0)h _(max) −b(x)h(x)]

In this particular embodiment the transition region between the yieldingportions and the end connections includes thickened segments which limitthe spread of plastic strain into the connection region.

This is example is intended to show one way in which the variablecross-section could be generated in accordance with the principles setforth in this description, and is not intended to limit the invention inany manner. As discussed earlier, the variable cross-section portioncould also be a linearly variable profile or be defined by a lower orderfunction that that described in this example.

Various other modifications may be made or alternatives implementedwithout departing from the invention, which is defined solely by theclaims that now follow.

What is claimed is:
 1. A structural yielding link comprising: a firstend having a means for connecting to a face of a first beam or columnand a second end having a means for connecting to a face of a secondbeam or column; a first variable cross-section portion and a secondvariable cross-section portion extending from said first end and fromsaid second end, respectively; a constant cross-section portion joiningsaid first variable cross-section portion and said second variablecross-section portion.
 2. The structural yielding link according toclaim 1 for use in an eccentrically braced frame arrangement or in alinked column frame arrangement.
 3. The structural yielding linkaccording to claim 1, wherein said first and said second variablecross-section portions are hollow along at least a portion of lengthsthereof.
 4. The structural yielding link according to claim 1, whereinsaid first variable cross-section portion and said second variablecross-section portion have a cross-section tapering from said respectivefirst and second end portions towards said constant cross-sectionportion such that a width of said first and second variablecross-section portions at said respective first and second end portionsis greater than a width at said constant cross-section portion.
 5. Thestructural yielding link according to claim 4, wherein said first andsaid second variable cross-section portions are hollow and have aninterior wall thickness which is greater at said first and second endportions, respectively than proximate said constant-cross sectionportion.
 6. The structural yielding link according to claim 1, whereinsaid variable cross-section portions are designed, sized and otherwisedimensioned to promote near simultaneous yielding along a substantialportion of the yielding link when subjected to a linearly varyingbending moment diagram.
 7. The structural yielding link according toclaim 1, wherein said first and said second variable cross-sectionportions have a width defined by a higher-order function; whereby saidhigher-order function promotes yielding of the link when the link issubjected to load(s) causing a linearly varying bending moment diagram.8. A structural link according to claim 1, wherein said first and saidsecond variable cross-section portions are defined such that the crosssectional area along the length of the link is constant; whereby saidconstant cross sectional area promotes a constant axial strain along thelength of the link when the link is subjected to any axial load.
 9. Astructural link according to claim 8, wherein said constant crosssectional area is achieved by a flange located at the flexural neutralaxis of the cross section.
 10. The structural yielding link according toclaim 1, further comprising a transition region between said first andsecond ends and said first and second variable cross-section portions,respectively; where said transition region includes a thickened materialportion for limiting stress and strain occurring during yielding of thelink from propagating to said means for connecting to said end faces ofsaid first and second beams.
 11. The structural yielding link accordingto claim 1, wherein said variable cross-section portions are designed,sized and otherwise dimensioned to promote yielding along a substantialportion of the yielding link.
 12. The structural yielding link accordingto claim 4, wherein said first and said second variable cross-sectionportions are hollow and have an interior wall thickness which isconstant throughout said first and second variable cross-sectionportions.
 13. The structural yielding link according to claim 1, whereinsaid first variable cross-section portion and said second variablecross-section portion have a cross-section tapering from said respectivefirst and second end portions towards said constant cross-sectionportion such that a depth of said first and second variablecross-section portions at said respective first and second end portionsis greater than a depth at said constant cross-section portion.
 14. Aneccentrically braced frame arrangement comprising a first column and asecond column; a beam connecting said first column and said secondcolumn; said beam having a first portion connected to said first column,a second portion connected to said second column and a yielding linkconnecting said first portion and said second portion; at least onebrace having a node end connected proximate an end of said first columnand another end connected to an end of said first portion proximate saidyielding link; wherein said yielding link comprises a first end having ameans for connecting to an end face of said first portion and a secondend having a means for connecting to an end face of said second portion;a first variable cross-section portion and a second variablecross-section portion extending from said first end and from said secondend, respectively; a constant cross-section portion joining said firstvariable cross-section portion and said second variable cross-sectionportion.
 15. The eccentrically braced frame arrangement according toclaim 14, wherein said first and said second variable cross-sectionportions are hollow along at least a portion of lengths thereof.
 16. Theeccentrically braced frame arrangement according to claim 14, whereinsaid first variable cross-section portion and said second variablecross-section portion have a cross-section tapering from said respectivefirst and second end portions towards said constant cross-sectionportion such that a width of said first and second variablecross-section portions at said respective first and second end portionsis greater than a width at said constant cross-section portion.
 17. Theeccentrically braced frame arrangement according to claim 16, whereinsaid first and said second variable cross-section portions are hollowand have an interior wall thickness which is greater at said first andsecond end portions, respectively than proximate said constant-crosssection portion.
 18. The eccentrically braced frame arrangementaccording to claim 14, wherein said variable cross-section portions aredesigned, sized and otherwise dimensioned to promote yielding along asubstantial portion of the yielding link.
 19. The eccentrically bracedframe arrangement according to claim 14, wherein said first and saidsecond variable cross-section portions have a width defined by ahigher-order function; whereby said higher-order function promotesyielding of the link when the link is subjected to load(s) causing alinearly varying bending moment diagram.
 20. An eccentrically bracedframe arrangement according to claim 14, wherein said first and saidsecond variable cross-section portions are defined such that the crosssectional area along the length of the link is constant; whereby saidconstant cross sectional area promotes a constant axial strain along thelength of the link when the link is subjected to any axial load.
 21. Aneccentrically braced frame arrangement according to claim 20, whereinsaid constant cross sectional area is achieved by a flange located atthe flexural neutral axis of the cross section.
 22. The eccentricallybraced frame arrangement according to claim 14, further comprising atransition region between said first and second ends and said first andsecond variable cross-section portions, respectively; where saidtransition region includes a thickened material portion for limitingstress and strain occurring during yielding of the link from propagatingto said means for connecting to said end faces of said first and secondbeams.
 23. The eccentrically braced frame arrangement according to claim14, wherein said variable cross-section portions are designed, sized andotherwise dimensioned to promote yielding along a substantial portion ofthe yielding link.
 24. The eccentrically braced frame arrangementaccording to claim 16, wherein said first and said second variablecross-section portions are hollow and have an interior wall thicknesswhich is constant throughout said first and second variablecross-section portions.
 25. The eccentrically braced frame arrangementaccording to claim 14, wherein said first variable cross-section portionand said second variable cross-section portion have a cross-sectiontapering from said respective first and second end portions towards saidconstant cross-section portion such that a depth of said first andsecond variable cross-section portions at said respective first andsecond end portions is greater than a depth at said constantcross-section portion.